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   "id": "dbba69a1",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "# Softmax Regression Implementation from Scratch\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "27f90605",
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    "execution": {
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    },
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    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfb91f54",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Given a matrix `X` we can sum over all elements (by default) or only\n",
    "over elements in the same axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4721b51f",
   "metadata": {
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    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[5., 7., 9.]]),\n",
       " tensor([[ 6.],\n",
       "         [15.]]))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "X.sum(0, keepdims=True), X.sum(1, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "878927e7",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "$$\\mathrm{softmax}(\\mathbf{X})_{ij} = \\frac{\\exp(\\mathbf{X}_{ij})}{\\sum_k \\exp(\\mathbf{X}_{ik})}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d2f22e34",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2023-08-18T19:40:41.776558Z"
    },
    "origin_pos": 9,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def softmax(X):\n",
    "    X_exp = torch.exp(X)\n",
    "    partition = X_exp.sum(1, keepdims=True)\n",
    "    return X_exp / partition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf65a513",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We turn each element\n",
    "into a nonnegative number.\n",
    "Each row sums up to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "90ec733c",
   "metadata": {
    "execution": {
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    "origin_pos": 12,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0.2511, 0.1417, 0.1158, 0.2529, 0.2385],\n",
       "         [0.2004, 0.1419, 0.1957, 0.2504, 0.2117]]),\n",
       " tensor([1., 1.]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.rand((2, 5))\n",
    "X_prob = softmax(X)\n",
    "X_prob, X_prob.sum(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35674906",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The softmax regression model.\n",
    "We flatten each image,\n",
    "treating them as vectors of length 784.\n",
    "Since our dataset has 10 classes,\n",
    "our network has an output dimension of 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6525b147",
   "metadata": {
    "execution": {
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    },
    "origin_pos": 20,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class SoftmaxRegressionScratch(d2l.Classifier):\n",
    "    def __init__(self, num_inputs, num_outputs, lr, sigma=0.01):\n",
    "        super().__init__()\n",
    "        self.save_hyperparameters()\n",
    "        self.W = torch.normal(0, sigma, size=(num_inputs, num_outputs),\n",
    "                              requires_grad=True)\n",
    "        self.b = torch.zeros(num_outputs, requires_grad=True)\n",
    "\n",
    "    def parameters(self):\n",
    "        return [self.W, self.b]\n",
    "\n",
    "@d2l.add_to_class(SoftmaxRegressionScratch)\n",
    "def forward(self, X):\n",
    "    X = X.reshape((-1, self.W.shape[0]))\n",
    "    return softmax(torch.matmul(X, self.W) + self.b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfaecfaa",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Create sample data `y_hat`\n",
    "with 2 examples of predicted probabilities over 3 classes and their corresponding labels `y`.\n",
    "Using `y` as the indices of the probabilities in `y_hat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "be06d72f",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2023-08-18T19:40:41.828524Z"
    },
    "origin_pos": 22,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1000, 0.5000])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = torch.tensor([0, 2])\n",
    "y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\n",
    "y_hat[[0, 1], y]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59bfdb99",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Implement the cross-entropy loss function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6f5696bf",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2023-08-18T19:40:41.832979Z",
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     "shell.execute_reply": "2023-08-18T19:40:41.845315Z"
    },
    "origin_pos": 26,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1.4979)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    return -torch.log(y_hat[list(range(len(y_hat))), y]).mean()\n",
    "\n",
    "cross_entropy(y_hat, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0d97074e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T19:40:41.850484Z",
     "iopub.status.busy": "2023-08-18T19:40:41.849744Z",
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     "shell.execute_reply": "2023-08-18T19:40:41.853500Z"
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   "outputs": [],
   "source": [
    "@d2l.add_to_class(SoftmaxRegressionScratch)\n",
    "def loss(self, y_hat, y):\n",
    "    return cross_entropy(y_hat, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a8430c3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Train the model with 10 epochs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0fed2d06",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2023-08-18T19:41:38.024988Z"
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    "origin_pos": 31,
    "tab": [
     "pytorch"
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      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = d2l.FashionMNIST(batch_size=256)\n",
    "model = SoftmaxRegressionScratch(num_inputs=784, num_outputs=10, lr=0.1)\n",
    "trainer = d2l.Trainer(max_epochs=10)\n",
    "trainer.fit(model, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "772a2a6b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Classify some images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ea0b6dd0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T19:41:38.030970Z",
     "iopub.status.busy": "2023-08-18T19:41:38.030251Z",
     "iopub.status.idle": "2023-08-18T19:41:38.207822Z",
     "shell.execute_reply": "2023-08-18T19:41:38.206713Z"
    },
    "origin_pos": 33,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([256])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = next(iter(data.val_dataloader()))\n",
    "preds = model(X).argmax(axis=1)\n",
    "preds.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41ef8291",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T19:41:38.211804Z",
     "iopub.status.busy": "2023-08-18T19:41:38.211212Z",
     "iopub.status.idle": "2023-08-18T19:41:38.569431Z",
     "shell.execute_reply": "2023-08-18T19:41:38.568219Z"
    },
    "origin_pos": 35,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 1200x150 with 8 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wrong = preds.type(y.dtype) != y\n",
    "X, y, preds = X[wrong], y[wrong], preds[wrong]\n",
    "labels = [a+'\\n'+b for a, b in zip(\n",
    "    data.text_labels(y), data.text_labels(preds))]\n",
    "data.visualize([X, y], labels=labels)"
   ]
  }
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